: , @ , /@ , .. , NFunction .

# Functional operators

These operators can help the user to program in the style of functional programming languages like Miranda and Haskell.

: | Prepend item to list, or concatenate strings
@ | Apply a function
/@ | Apply a function to all entries in a list
.. | Construct a list of consecutive integers
NFunction | make wrapper for numeric functions

###

: -- Prepend item to list, or concatenate strings

Standard math library

##### Calling format:

    item : list (prec. 7)
    string1 : string2 (prec. 7)

##### Parameters:

`item` -- an item to be prepended to a list

`list` -- a list

`string1` -- a string

`string2` -- a string

##### Description:

The first form prepends "item" as the first entry to the list "list". The second form concatenates the strings "string1" and "string2".

##### Examples:

    In> a:b:c:{}
    Out> {a,b,c};
    In> "This":"Is":"A":"String"
    Out> "ThisIsAString";

##### See also:

Concat , ConcatStrings .

###

@ -- Apply a function

Standard math library

##### Calling format:

    fn @ arglist (prec. 60)

##### Parameters:

`fn` -- function to apply

`arglist` -- single argument, or a list of arguments

##### Description:

This function is a shorthand for `Apply`. It applies the function "fn" to the argument(s) in "arglist" and returns the result. The first parameter "fn" can either be a string containing the name of a function or a pure function.

##### Examples:

    In> "Sin" @ a
    Out> Sin(a);
    In> {{a},Sin(a)} @ a
    Out> Sin(a);
    In> "f" @ {a,b}
    Out> f(a,b);

##### See also:

Apply .

###

/@ -- Apply a function to all entries in a list

Standard math library

##### Calling format:

fn /@ list (prec. 60)

##### Parameters:

`fn` -- function to apply

`list` -- list of arguments

##### Description:

This function is a shorthand for `MapSingle`. It successively applies the function "fn" to all the entries in "list" and returns a list contains the results. The parameter "fn" can either be a string containing the name of a function or a pure function.

##### Examples:

    In> "Sin" /@ {a,b}
    Out> {Sin(a),Sin(b)};
    In> {{a},Sin(a)*a} /@ {a,b}
    Out> {Sin(a)*a,Sin(b)*b};

##### See also:

MapSingle , Map , MapArgs .

###

.. -- Construct a list of consecutive integers

Standard math library

##### Calling format:

    n .. m (prec. 60)

##### Parameters:

`n` -- integer. the first entry in the list

`m` -- integer, the last entry in the list

##### Description:

This command returns the list `{n, n+1, n+2, ..., m}`. If `m` is smaller than `n`, the empty list is returned. Note that the `..` operator should be surrounded by spaces to keep the parser happy, if "n" is a number. So one should write "`1 .. 4`" instead of "`1..4`".

##### Example:

    In> 1 .. 4
    Out> {1,2,3,4};

##### See also:

Table .

###

NFunction -- make wrapper for numeric functions

Standard math library

##### Calling format:

    NFunction("newname","funcname", {arglist})

##### Parameters:

"newname" -- name of new function

`"funcname"` -- name of an existing function

`arglist` -- symbolic list of arguments

##### Description:

This function will define a function named "newname" with the same arguments as an existing function named "funcname". The new function will evaluate and return the expression "funcname(arglist)" only when all items in the argument list `arglist` are numbers, and return unevaluated otherwise.

This can be useful when plotting functions defined through other Yacas routines that cannot return unevaluated.

##### Example:

Suppose we need to define a complicated function `t(x)` which cannot be evaluated unless `x` is a number:

    In> t(x) := If(x<=0.5, 2*x, 2*(1-x));
    Out> True;
    In> t(0.2);
    Out> 0.4;
    In> t(x);
    In function "If" :
    bad argument number 1 (counting from 1)
    CommandLine(1) : Invalid argument

Then, we can use `NFunction()` to define a wrapper `t1(x)` around `t(x)` which will not try to evaluate `t(x)` unless `x` is a number.

    In> NFunction("t1", "t", {x})
    Out> True;
    In> t1(x);
    Out> t1(x);
    In> t1(0.2);
    Out> 0.4;

Now we can plot the function.

    In> GnuPlot(-0.1, 1.1, 30, t1(x))
    Out> True;

##### See also:

MacroRule .